Data-driven approaches to dynamical systems have been widely investigated recently [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}.
They enable us to understand the dynamics using given time-series data without knowing the underlying dynamical system that generates the data.
In particular, the application of Koopman operator theory for this purpose has attracted much attention [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}.
The Koopman operator gives a lifted representation of a nonlinear dynamical system.
Since the Koopman operator is linear even though the original system is nonlinear,
we can use linear algebra to analyze the behaviors of the dynamics with given data.
One successful application of Koopman operator theory to data analysis is dynamic mode decomposition (DMD) and extended DMD (EDMD) [10]}, [13]}, [14]}.
We can decompose observables of the system by using the eigenvalues and eigenfunctions of the Koopman operator and extract the long-term behavior of the system.
Using DMD and EDMD, we can extract the Koopman eigenvalues and eigenfunctions from time-series data and predict long-term behaviors.
Koopman operator theory has also been applied to network dynamics.
However, most existing works do not focus on the data-driven setting or require partial information about the dynamical system [25]}, [26]}, [27]}, [28]}.
